Overview
- Group
- SmallGroup(128,161)
- Rank
- 2
- Schläfli Type
- {64}
- Vertices, edges, …
- 64, 64
- Order of s0s1
- 64
- Also known as
- 64-gon, {64}. if this polytope has another name.
Special Properties
- Universal
- Spherical
- Locally Spherical
- Orientable
- Self-Dual
Quotients maximal quotients in bold
2-fold
4-fold
8-fold
16-fold
32-fold
Covers minimal covers in bold
2-fold
3-fold
4-fold
5-fold
6-fold
7-fold
9-fold
10-fold
11-fold
13-fold
14-fold
15-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 3, 4)( 5, 7)( 6, 8)( 9,13)(10,14)(11,16)(12,15)(17,25)(18,26)(19,28)(20,27)(21,31)(22,32)(23,29)(24,30)(33,49)(34,50)(35,52)(36,51)(37,55)(38,56)(39,53)(40,54)(41,61)(42,62)(43,64)(44,63)(45,57)(46,58)(47,60)(48,59);; s1 := ( 1,33)( 2,34)( 3,36)( 4,35)( 5,39)( 6,40)( 7,37)( 8,38)( 9,45)(10,46)(11,48)(12,47)(13,41)(14,42)(15,44)(16,43)(17,57)(18,58)(19,60)(20,59)(21,63)(22,64)(23,61)(24,62)(25,49)(26,50)(27,52)(28,51)(29,55)(30,56)(31,53)(32,54);; poly := Group([s0,s1]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1");;
s0 := F.1;; s1 := F.2;;
rels := [ s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(64)!( 3, 4)( 5, 7)( 6, 8)( 9,13)(10,14)(11,16)(12,15)(17,25)(18,26)(19,28)(20,27)(21,31)(22,32)(23,29)(24,30)(33,49)(34,50)(35,52)(36,51)(37,55)(38,56)(39,53)(40,54)(41,61)(42,62)(43,64)(44,63)(45,57)(46,58)(47,60)(48,59); s1 := Sym(64)!( 1,33)( 2,34)( 3,36)( 4,35)( 5,39)( 6,40)( 7,37)( 8,38)( 9,45)(10,46)(11,48)(12,47)(13,41)(14,42)(15,44)(16,43)(17,57)(18,58)(19,60)(20,59)(21,63)(22,64)(23,61)(24,62)(25,49)(26,50)(27,52)(28,51)(29,55)(30,56)(31,53)(32,54); poly := sub<Sym(64)|s0,s1>;
Finitely Presented Group Representation (Magma)
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References
None.
to this polytope.